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Abstract
In this study, we will prove that the presence of the voids and of the internal state variables in an elastic body with dipolar structure have no effect on the result of uniqueness regarding the solution of the initial-boundary value problem from this context. First, we put down the basic equations and conditions which define the initial-boundary value problem in the context. Then, by means of three theorems, we prove some auxiliary estimates that underlie the result of uniqueness. Finally, by means of these estimates and by using the Gronwall’s inequality, we prove our main result.
Highlights
IntroductionThere has been a significant increase of the number of studies dedicated to the theory of porous media
We want to argue the motivation for considering the voids of material
We will address the problem of the influence that voids and internal state variables may have on the behavior of media with dipolar structure
Summary
There has been a significant increase of the number of studies dedicated to the theory of porous media This is why we have included our present study in the elasticity of media with voids or vacuous pores. In our paper we consider a dipolar structure, as a particular case of the microstructure, which was introduced by Eringen. For this we can enumerate the papers [7,8]. The number of studies dedicated to theory of bodies with internal state variables has increased. The internal state variables were considered to describe the evolution of the viscoelastic bodies in the theory of thermoelasticity (see, for instance, Chirita [23]). For some results on anti-plane states in an anisotropic elastic body and for orthotropic or isotropic plates, we suggest [30,31]
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